Imaging of Local Rough Surfaces by the Linear Sampling Method with Near-Field Data

Abstract

Consider the scattering of a time-harmonic point source from an unbounded rough surface. The surface is assumed to be different from a plane surface over a finite interval, which leads to the situation that the model problem can be reduced to an equivalent boundary value problem with compactly supported boundary data. Well-posedness is thus proved by employing the variational method with classical Fredholm theory. By constructing a modified near-field equation, we then propose a novel sampling-type method for reconstructing the shape and location of the local rough surface, yielding a fast imaging algorithm. Numerical experiments are presented to illustrate the effectiveness of the method.